The iterated Carmichael lambda function

Abstract

The Carmichael lambda function λ(n) is defined to be the smallest positive integer m such that a m is congruent to 1 modulo n, for all a and n relatively prime. The function λ k (n) is defined to be the kth iterate of λ(n). Previous results show a normal order for n/λ k (n) where k = 1, 2. We will show a normal order for all k.